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I'm running linear regression model on a post-intervention test score controlling for pre-intervention test score. I used Box-Cox transformation on the post-intervention test score to normalize it. Since there no normality assumption imposed on independent variable, I plan not to transform the pre-intervention test score; but since the pre- and post-test are on a same scale, should I transform the pre-test as well just to be consistent?

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  • $\begingroup$ Bear in mind that inferences on transform data cannot be validly applied to non-transformed data because $f(\sigma^{2}_{X}) \ne \sigma^{2}_{f(X)}$. So if you find statistical evidence that $f(X) \ne f(Y)$ you did not just find statistical evidence that $X \ne Y$. $\endgroup$
    – Alexis
    Jul 24, 2014 at 17:22
  • $\begingroup$ A similar question with answer Skewness transformation for one but not the other variable? $\endgroup$ Feb 5 at 12:52

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I'd say yes, you should use the same transformation on both -- largely for a non-technical reason: You're going to have to explain your analysis to somebody. Since the pre- and post-scores are on the same scale, it's just kinda weird not to keep them on the same scale.

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